Three-dimensional ageostrophic motion in mesoscale vortex dipoles

The three-dimensional motion of mesoscale baroclinic dipoles is simulated using a nonhydrostatic Boussinesq numerical model. The initial conditions are two ellipsoidal vortices of positive and negative potential vorticity anomalies. The flow is moderately ageostrophic with a maximum absolute Rossby number equal to 0.71. The trajectory of the dipole is related to the maximum potential vorticity anomaly and size of the vortices. Three cases are considered depending on the curvature of the dipole trajectory: negative, close to zero, and positive. The ageostrophic flow strongly depends on the distance between the ellipsoidal vortices d0. For small d0 the vortices move steadily as a compact dipole, and the vertical velocity w has an octupolar three-dimensional pattern. The horizontal ageostrophic velocity is due to the advective acceleration of the flow, particularly the centripetal acceleration. The speed acceleration is only relatively important at the rear and front parts of the dipole axis, where the flow curvature is small but where the flow confluence and diffluence are, respectively, large. The geostrophy is maximal at the dipole center, on the dipole axis, where both curvature and speed acceleration are minimal. As d0 increases, the dipole self-propagating velocity and the extreme values of |w| decrease, and vortex oscillations highly distort the octupolar pattern of w. In all cases, as is typical of balanced mesoscale geophysical flows, the vertical velocity is related to the advection of vertical vorticity by the horizontal shear velocity.